Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<n;++i)

using namespace std;

typedef pair<int,int>P;

struct edge{
	int to;
	int cost;
};

const int MAX_N = 100005;

int sdir[MAX_N];
int tdir[MAX_N];
int spt[MAX_N];
int tpt[MAX_N];
map<P,int> mp;
vector<int> G[MAX_N];

void bfs(int u,int* flag)
{
    queue<P> que;
    que.push(P(u,0));
    while(!que.empty()){
        P p = que.front();
        que.pop();
        rep(i,G[p.first].size()){
            if(flag[G[p.first][i]] > p.second + 1){
                flag[G[p.first][i]] = p.second + 1;
                que.push(P(G[p.first][i],flag[G[p.first][i]]));
            }
        }
    }
    return;
}

int main()
{
    int n,m,s,t;
	scanf("%d%d%d%d",&n,&m,&s,&t);
	rep(i,m){
		int x,y;
        scanf("%d%d",&x,&y);
        G[x-1].push_back(y-1);
        G[y-1].push_back(x-1);
        mp[P(x-1,y-1)]++;
        mp[P(y-1,x-1)]++;
	}
    fill(sdir,sdir+n,INF);
    fill(tdir,tdir+n,INF);
    bfs(s-1,sdir);
    sdir[s-1] = 0;
    bfs(t-1,tdir);
    tdir[t-1] = 0;
    rep(i,n){
        if(sdir[i] != INF && tdir[i] != INF){
            spt[sdir[i]]++;
            tpt[tdir[i]]++;
        }
    }
    int min_dir = sdir[t-1];
    ll res = 0;
    rep(i,min_dir-1){
        res += (ll)spt[i] * tpt[min_dir - i - 2];
    }
    printf("%lld\n",res);
	return 0;
}